Calculation method for thickness of inner oxide layer of martensitic heat-resistant steel in steam environment

This application claims priority to Chinese Patent Application No. 202310439946.7, filed on Apr. 20, 2023. The disclosures of the above-mentioned applications are incorporated herein by reference in their entireties.

The present application belongs to the technical field of martensitic heat-resistant steels, and particular to a calculation method for a thickness of an inner oxide layer of a martensitic heat-resistant steel in steam environment.

Martensitic heat-resistant steels include T/P91, T/P92, E911, T/P93 (9Cr-3W-3Co), T/P122 and other 9-12% Cr heat-resistant steels. Martensitic heat-resistant steel has excellent high-temperature creep strength, good thermal conductivity and low coefficient of linear expansion, and is widely used in the manufacture of super critical units of the main steam pipe, a collector box, a superheater, a reheater and other important high-temperature components. As the working steam pressure of the unit increases, the steam oxidation resistance of the martensitic heat-resistant steel becomes one of the key factors affecting the life of high-temperature components. In the long-term operation of high-temperature components, because the growth of the thickness of the oxide layer will lead to a reduction in the effective wall thickness of the pipe wall, the stress on the pipe wall also is increased accordingly; at the same time, the oxidation layer causes the thermal conductivity of the pipe wall to deteriorate, so that the average operation temperature of the pipe wall is increased, if it is in over-temperature service state for long time, when the development to a certain extent, eventually the pipe will burst. Therefore, to assess the service life of the components can achieve early warning to reduce accidents, it is necessary to predict the thickness of the oxide layer of the superheater, reheater and other components in service in steam environment.

To calculate the thickness of the inner layer of the oxide film, it is necessary to use the oxidation kinetic model of heat-resistant steel in the steam environment. The current domestic and foreign steam oxidation kinetic model of the martensitic heat-resistant steel generally only considers the effect of steam temperature, rarely consider the effect of the changes in steam pressure, especially doesn't consider the coupling effect of the two. In fact, the steam temperature and the steam pressure in different components of the unit vary greatly, for example, the steam temperature of the high temperature reheater is higher than that of the superheater, but the steam pressure is significantly lower than that of the superheater. Therefore, only by considering the comprehensive effects of the steam temperature and the steam pressure can we accurately predict the thickness of the oxide layer of different components and thus their remaining life. In addition, most of the current steam oxidation kinetic models for martensitic heat-resistant steels are based on the experimental results of the oxidation weight gain method, which cannot directly calculate the thickness of the oxide layer. Although a few papers have reported high-temperature steam oxidation kinetic models for martensitic heat-resistant steels based on the growth of the thickness of the oxide layer, the oxide layer includes both the inner layer and the outer layer, and these papers do not distinguish between the thickness of the outer layer and the thickness of the inner layer. The Applicant's study shows that only the growth of the thickness of the inner layer leads to a thinning of the thickness of the pipe wall, which affects the pipe's life, so that predicting the thickness of the inner layer is more practical importance.

In order to solve the problems in the related art, the present application provides a calculation method for thickness of inner oxide layer of a martensitic heat-resistant steel in steam environment, which can easily and quickly calculate the thickness of the inner oxide layer of 9% Cr martensitic heat-resistant steel in steam environment based on the steam temperature, the steam pressure and the operation time, thus the calculation accuracy is significantly improved, and the remaining life of the high-temperature components can be assessed in the actual operation of the power plant without cutting the pipe, the safe operation of the unit is ensured and the cost is reduced, and it has important industrial application value.

In order to achieve the above purpose, the present application adopts the following technical solutions.

The present application provides a calculation method for a thickness of an inner oxide layer of a martensitic heat-resistant steel in steam environment, the martensitic heat-resistant steel is 9% Cr heat-resistant steel, and the thickness of inner oxide layer in steam environment is calculated by a formula:

In an embodiment, the steam temperature is from 550 to 650° C. and the steam pressure is from 5.0 to 25.0 MPa.

In an embodiment, the operation time t is from 1,000 to 150,000 h.

In an embodiment, in the formula for calculating Y, in response to that the steam temperature T is less than 600° C., ω is 0.1682±0.1136; in response to that the steam temperature T is not less than 600° C., ω is 0.6891±0.2269.

In an embodiment, in the formula for calculating YT, n is equal to 0.25.

In an embodiment, in the formula for calculating YT, the mathematical relationship between the fitting coefficient k and the steam temperature T is1.01×10.

In an embodiment, in the formula for calculating YT, the mathematical relationship between the activation energy Q and the time t is106661.33557−0.364983.07915×10.

In an embodiment, in the formula for calculating Yp, the fitting coefficient a is 22.21, the fitting coefficient b is 0.0009334, the fitting coefficient c is −0.8198, the fitting coefficient d is −7.655×10-10, the fitting coefficient h is 1.79×10-5, and the fitting coefficient i is 0.1152.

The present application provides an application of the calculation method as mentioned above on assessing a life of a martensitic heat-resistant steel component operating in steam environment in power plant.

According to the above-mentioned scheme, the steam temperature is from 550 to 650° C. and the steam pressure is from 5.0 to 25.0 MPa.

In the present application, the relationship between inner oxide thickness Y and steam temperature T or steam pressure p is studied separately, and then a weighting analysis of the degree of temperature and pressure affecting the thickness of the inner oxide layer is performed. It is found that the weight of temperature on the thickness of the inner oxide layer varies in different temperature ranges under the coupling effect of steam temperature and steam pressure. Finally, the formula is mathematically modified based on the traditional exponential function model by combining the actual data, and a formula for calculating the thickness of the inner oxide layer of 9% Cr martensitic heat-resistant steel is proposed that integrates the three factors: steam temperature, steam pressure and operation time. It is not necessary to cut the pipe for measurement, achieving cost savings and estimation of the thickness of the inner oxide layer of the pipe without affecting operation. In addition, by calculating the thickness of the inner oxide layer of 9% Cr martensitic heat-resistant steel by this formula, it can accurately reflect the degree of oxidation and corrosion of the inner wall of the pipe, and provide basic data for calculating the remaining life of the component.

The present application has the beneficial effects of:

The technical solutions of the present application are further explained and illustrated by specific embodiments below.

(1) The Relationship Between the Thickness of the Inner Oxide Layer YT and the Temperature T.

To explore the effect of temperature T and time t on the oxide layer of high temperature heating surface of the power plant boiler, the thickness of the inner oxide layer YT and temperature T in high temperature conditions conforms to the following exponential function law:

A large amount of data from the actual power plant and the simulation experiments in the laboratory is collected in the embodiment of the present application, including the thickness of the inner oxide layer of 9% Cr heat-resistant steel such as T/P91 and T/P92 at the temperature from 550° C. to 650° C. and at the steam pressure from 5.0 to 25.0 MPa for the oxidation time from 1,000 to 150,000 h; the parameters n, Q, and k in the formula (1) are calculated by using the above data. The calculation method is shown below:

Step 1: calculating n.

When a specific temperature T is taken, kexp

is a constant. When the pressure is certain, the experimental data at each temperature is substituted into the formula for fitting, and the fitting results of two different sets of data as follows.

The first set:

The second set:

It can be found that n is from about 0.21 to 0.35 and fluctuates around 0.25, indicating that the oxidation kinetics of 9% Cr heat-resistant steel basically obey the cubic law, so n is taken as 0.25, and then the formula (1) is modified as follows

Step 2: calculating the activation energy Q.

Making logarithmic transformation on both sides of formula (2) to obtain

When a specific time t is taken, then ln(kt) is a constant and is noted as G. The above formula is simplified to

When t is equal to 1,000 h, 10,000 h, 50,000 h, 100,000 h, 150,000 h, the experimental data are substituted into the fitting formula obtained in step 1, and the values lnY are calculated for T equal to 550° C., 575° C., 600° C., 625° C., 650° C., respectively, and then substituted back to the formula (3) to calculate the activation energy Q for different times t as shown in Table 1.

From Table 1, it can be seen that the Q differs at different times, indicating that the activation energy of the oxidation reaction varies at different times. It is found that the oxidation reaction of 9% Cr heat-resistant steel is a complex and dynamic process. The composition and structure of the oxidation products and oxidation mechanism vary at different stages of the reaction. Therefore, the present application uses a mathematical model to fit the variation of the activation energy with time and obtains that the activation energy Q with time t is highly consistent with the following mathematical model, the formula is:106661.33557−0.364983.07915×10  (4).

Substituting the formula (4) back into the formula (2), the corrected thickness formula is:

Step 3, calculating the coefficient k.

A specific temperature T and the operation time t are selected, then

is a constant value and is recorded as Z, then the above formula is changed to YT=k*Z. The experimental data at each temperature is substituted into the formula (5) in turn and fitted to obtain the coefficient k. It is found that the k varies at different temperatures, the fitted curve is shown in the, and the results are:

The relationship between the k and temperature T is obtained as:1.01×10−4214.68  (6).

It can be seen that as the temperature increases, the k becomes larger. This indicates that the higher the temperature, the greater the influence of temperature on the thickness of the inner oxide layer. Therefore, finally, the fitting formula for the thickness of the inner oxide layer YT and the temperature T is

In the above formula, the unit of the temperature T is K, the unit of the time t is h, and the unit of the calculated thickness of the inner oxide layer YT is μm.

(2) The Relationship Between the Thickness of the Inner Oxide Layer Yp and the Steam Pressure p.

To investigate the influence of the pressure p and the time t on the formation of the oxide layer on the high temperature heating surface of the power plant boiler, the experimental data about the thickness of the inner oxide layer of 9% Cr martensitic heat-resistant steel at different time t and different pressure p is filtrated and processed, the results are shown in Table 2: